Space of modular forms of level 12, weight 3, and Character 12.c

• Label: 12.3.c
• Level: $12$
• Weight: $3$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(12, [\chi])\).

	Total	New	Old
Modular forms	7	1	6
Cusp forms	1	1	0
Eisenstein series	6	0	6

Trace form

q - 3 * q^3 + 2 * q^7 + 9 * q^9 - 22 * q^13 + 26 * q^19 - 6 * q^21 + 25 * q^25 - 27 * q^27 - 46 * q^31 + 26 * q^37 + 66 * q^39 - 22 * q^43 - 45 * q^49 - 78 * q^57 + 74 * q^61 + 18 * q^63 + 122 * q^67 - 46 * q^73 - 75 * q^75 - 142 * q^79 + 81 * q^81 - 44 * q^91 + 138 * q^93 + 2 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.3.c.a	$12$	$3$	12.c	3.b	$2$	$1$	$1$	$0.327$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓	✓	✓	12.3.c.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(2\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)